A method of enhancing the efficiency of entangled biphoton sources based on a type II femtosecond spontaneous parametric downconversion (SPDC) process is proposed and implemented experimentally. Enhancement is obtained by mode inversion of one of the SPDC output beams, which allows the beams to overlap completely, thus maximizing the number of SPDC photon pairs with optimum spatiotemporal overlap. By use of this method, biphoton count rates as high as 16 kHz from a single 0.5-mm-long β-barium borate crystal pumped by second-harmonic radiation from a Ti:sapphire laser were obtained.